Let A = {1,2,3,5,6,7} and B = {2,4,6,8,9}. Find

(1) Write the following sets using the roster form:

(a) {x ∈ Z|10 ≤ x 2 < 100} (Careful, that is Z, not N!)

(b) {x ∈ N|x ≤ 4} (Remember that, in this text anyhow, 0 ∈ N.)

(2) Use set-builder notation to give a description of each set.

(a) {4,8,12}.

(b) {−2,0,2,4,6}.

(3) Let A = {1,2,3,5,6,7} and B = {2,4,6,8,9}. Find

(a) A ∩ B

(b) A ∪ B

(c) A − B

(d) B − A

(4) Draw Venn diagrams for A ∩ (B ∪ C) and (A ∩ B) ∪ (A ∩ C) to show that A ∩ (B ∪ C) =

(A ∩ B) ∪ (A ∩ C).

(5) Let A = {1,2,3,4} × {1,2,3}. List the elements of the set B = {(s,t) ∈ A|s ≥ t}.

(6) (bonus) Is the proposition Every element of the empty set has three toes true or false? Ex-

plain your answer! Hint: In symbols, the proposition i

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